Duality Results for a Class of Constrained Robust Nonlinear Optimization Problems

Savin Treanţă () and Tareq Saeed ()
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Savin Treanţă: Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
Tareq Saeed: Nonlinear Analysis and Applied Mathematics—Research Group, Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2022, vol. 11, issue 1, 1-17

Abstract: In this paper, we establish various results of duality for a new class of constrained robust nonlinear optimization problems. For this new class of problems, involving functionals of (path-independent) curvilinear integral type and mixed constraints governed by partial derivatives of second order and uncertain data, we formulate and study Wolfe, Mond-Weir and mixed type robust dual optimization problems. In this regard, by considering the concept of convex curvilinear integral vector functional , determined by controlled second-order Lagrangians including uncertain data, and the notion of robust weak efficient solution associated with the considered problem, we create a new mathematical context to state and prove the duality theorems. Furthermore, an illustrative application is presented.

Keywords: multi-objective robust control problem; robust duality; uncertain data; robust feasible solution; robust weak efficient solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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